1ST-ORDER THEORY OF WEAKLY ECCENTRIC ORBITAL MOTION

Starting from the analytical theory of perturbed circular motions pres ented in ''Celestial Mechanics'' (Bois, 1994), this paper presents an extended resolution valid also for small eccentricity orbits. The solu tion is of the first order of a small parameter characterizing the mag nitude of disturbing forces. The solution has the form of Fourier seri es with the coefficients given by iterative formation laws. The soluti on is free from singularities due to small eccentricity or inclination . As an example of numerical application the equatorial artificial sat ellite orbits are analyzed. For some high satellite orbits with small eccentricity the difference between the numerical integration and the analytical model does not exceed few centimeters per one revolution.